Simplify the following expression: $ z = \dfrac{2y + 2}{-10y + 8} - \dfrac{-9}{4} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{2y + 2}{-10y + 8} \times \dfrac{4}{4} = \dfrac{8y + 8}{-40y + 32} $ Multiply the second expression by $\dfrac{-10y + 8}{-10y + 8}$ $ \dfrac{-9}{4} \times \dfrac{-10y + 8}{-10y + 8} = \dfrac{90y - 72}{-40y + 32} $ Therefore $ z = \dfrac{8y + 8}{-40y + 32} - \dfrac{90y - 72}{-40y + 32} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{8y + 8 - (90y - 72) }{-40y + 32} $ Distribute the negative sign: $z = \dfrac{8y + 8 - 90y + 72}{-40y + 32}$ $z = \dfrac{-82y + 80}{-40y + 32}$ Simplify the expression by dividing the numerator and denominator by -2: $z = \dfrac{41y - 40}{20y - 16}$